Worksheet: Acceleration due to Gravity

In this worksheet, we will practice calculating the properties of the motion of an object that moves under constant acceleration due to gravity.

Q1:

A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial
vertically downward velocity of 1.40 m/s
and observes that it takes 1.80 s to reach the water.
How high above the water was the preserver released?

Q2:

A kangaroo can jump over an object
2.50 m high.

What is the initial vertically upward speed of the kangaroo that jumps over the object?

How much time is the kangaroo in the air for during its jump over the object?

Q3:

Suppose that a person takes 0.35 s
to react and move his hand to catch an object he has dropped. Assume that acceleration
due to gravity on Earth is 9.8 m/s2.

How far does the object fall on Earth?

How far does the object fall on the Moon, where the acceleration due to gravity is one sixth of that on Earth?

Q4:

A very strong, but inept, shot putter puts the shot straight up vertically with an initial
velocity of 11.0 m/s.
How much time does he have to get out of the way of the shot if it was
released at a height of 2.20 m
and he is 1.80 m tall?

Q5:

Standing at the base of one of the cliffs of Mt. Arapiles in Victoria, Australia, a
hiker of height 1.60 m hears a rock break loose
directly overhead. The rock breaks loose
132 m above the ground. The hiker sees
the rock 1.10 s after it breaks away.

How far above the hiker is the rock when he sees it?

How much time does he have to move before the rock hits his head?

Q6:

A basketball referee tosses the ball straight up for the starting tip-off. With what vertical upward speed must a basketball player leave the ground to rise 1.44 m above the floor in an attempt to get the ball?

Q7:

A basketball player jumps vertically upward from the floor.

Calculate the time spent in the air for a jump to a height of 1 meter.

Calculate the time spent in the air for a jump to a height of 0.3 meters.

Q8:

An object is dropped from a height of ℎ m. During the last 1.00 s of the object’s descent, it moves a distance ℎ3 m. Calculate the height ℎ.

Q9:

You throw a ball vertically upward with an initial velocity of 11.3 m/s. It passes a
tree branch on the way up at a height of 4.33 m above the point at which the ball
was thrown. How much time elapses before the ball again passes the tree branch (this
time on the way back down)?

Q10:

A steel ball is dropped onto a hard floor from a height of 2.10 m. The ball rebounds to a height of 1.33 m.

Calculate the magnitude of the velocity of the ball as it strikes the floor.

Calculate the magnitude of the velocity resulting from the rebound.

The ball is in contact with the floor for 6.67×10 s. What was the magnitude of the ball’s acceleration during contact with the floor?

A5.54×10 m/s2

B4.02×10 m/s2

C1.96×10 m/s2

D2.22×10 m/s2

E1.73×10 m/s2

Q11:

A coin is dropped from a hot-air balloon that is 356 m above the ground and rising at 12.3 m/s vertically upward. Assume that vertically upward displacement corresponds to positive values.

Find the distance between the coin and the ground 3.07 s after being released.

Find the velocity of the coin 3.07 s after being released.

Find the time before the coin hits the ground.

Q12:

An object is dropped from a height of 75.0 m above ground level.

Determine the distance traveled during time 𝑡, between 𝑡=0 and
𝑡=1.0s.

Determine the final velocity at which the object hits the ground.

Determine the distance traveled during the last 1.00 second of motion before hitting the ground.

Q13:

A diver bounces straight up from a diving board,
avoiding the diving board on the way down, and falls feet
first into a pool. She starts with a velocity of 4.00 m/s
and
her takeoff point is 1.80 m above the pool.

What is her highest point above the board?

How long a time are her
feet in the air?

What is her velocity when her feet hit the
water?

Q14:

A climber throws a rock into the sky from the top of a cliff, releasing the rock at a point 𝑃.
The rock has an initial vertical velocity of 9.71 m/s,
where positive velocity corresponds to vertically upward motion.
It takes 2.72 s
for the rock to hit the ground at the bottom of the cliff.

Calculate the vertical displacement of the rock from 𝑃 to the point where it hits the ground.

How long would it take for the rock to reach the ground if it is thrown, from 𝑃,
with an initial vertical velocity of
−9.71 m/s?

Q15:

A rock is thrown vertically downward with an initial speed of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water. Consider vertically upward displacement as positive-valued.

Calculate the rock’s displacement 0.500 s after release.

Calculate the rock’s displacement 1.00 s after release.

Calculate the rock’s displacement 1.50 s after release.

Calculate the rock’s displacement 2.00 s after release.

Calculate the rock’s displacement 2.50 s after release.

Calculate the rock’s velocity 0.500 s after release.

Calculate the rock’s velocity 1.00 s after release.

Calculate the rock’s velocity 1.50 s after release.

Calculate the rock’s velocity 2.00 s after release.

Calculate the rock’s velocity 2.50 s after release.

Q16:

A chunk of ice breaks off a
glacier and falls 30.0 m before it hits the water. Assuming drag forces are
negligible, how much time passes before the chunk hits the water?

Q17:

A ball is thrown vertically upward with an initial velocity of 18.5 m/s. The point of
release is the position 𝑦=0.00m. Take displacements from the release position. Assume
upward displacement corresponds to positive values.

What is the displacement of the ball at 𝑡=0.667s?

What is the displacement of the ball at 𝑡=1.11s?

What is the displacement of the ball at 𝑡=1.33s?

What is the displacement of the ball at 𝑡=2.25s?

What is the velocity of the ball at 𝑡=0.667s?

What is the velocity of the ball at 𝑡=1.11s?

What is the velocity of the ball at 𝑡=1.33s?

What is the velocity of the ball at 𝑡=2.25s?

Q18:

A ball is thrown straight up.
It passes a 2.00 m high window 7.50 m off the ground on its way up and takes
1.30 s to go past the window. What was the ball’s initial
velocity?

Q19:

A hot-air balloon rises from ground level at a constant velocity of 3.00 m/s.
60.0 seconds after liftoff,
a sandbag is dropped accidentally from the balloon.

Calculate the time it takes for the sandbag to reach the ground.

Calculate the velocity of the sandbag when it hits the ground.

Q20:

While observing a spacecraft land on a distant asteroid,
scientists noticed that the craft was falling at a rate of
5 m/s.
When it was
100 m
closer to the surface of the asteroid,
the craft reported a velocity of
8 m/s.
According to their data,
what is the approximate gravitational acceleration on this asteroid?

Q21:

A gray squirrel falls from a tree to the ground.
It falls from a height of
3.0 m.

What is the squirrel’s velocity just before hitting the ground?
Ignore the effect of air resistance.

If the squirrel stops at a distance of
2.0 cm
through bending its limbs, what is its deceleration?

Q22:

A small rocket with a booster blasts off vertically upward. When at a height of
5.00 km and velocity of
200.0 m/s, the
rocket releases its booster stage. The rocket continues to accelerate upward, while the
booster stage is accelerated only by gravity.

What is the maximum height that the booster stage reaches?

What is the speed of the booster stage when it is at a height of
6.00 km?

Q23:

The height of a ball falling from the roof of a building that is
98 meters high to
the street below, at 1.0-second intervals, is shown in the diagram. The ball has a
vertically downward speed of
4.9 m/s at the instant
time 𝑡=0.0s.